Question

A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?

• A. Circle
• B. Hyperbola
• C. Ellipse
• D. Straight line

Answer 1

Answer: (B)

Hyperbola

Answer 2

The correct answer is option (B): Hyperbola

A(2h,0), B(0,2k)

Area of $\Delta$OAB=8

$\frac{1}{2}\times 2h\times 2k=8$

$hk=4$

Locus of XY = 4